Bridgham et al (2009) are interested in the reversibility of evolution, and discuss their results in terms of something called "Dollo's law." Louis Dollo, an early 20th century paleobiologist, was interested in discerning phylogenies. He maintained that one could always distinguish ancestral forms from descendant forms. Stephen Jay Gould (1970) commented that Dollo's "law" was not an empirical observation, but rather a postulate which he felt was necessary to properly construct phylogenies. Over the years the meaning of "Dollo's law" transmogrified. In modern usage, the phrase has come to mean that complex traits, once lost, do not re-evolve in the same lineage. For example, whales do not re-evolve gills, even though they are aquatic creatures who descended from fish, because gills are a lost, complex trait in that lineage.

Dollo's law is taken with a grain of salt by many biologists, and apparent exceptions to the law have been noted (cited in Bridgham et al 2009). Nonetheless, although Dollo's law isn't very reliable at the organismal level, maybe it can do better at the molecular level. Bridgham et al (2009) wanted to test that idea:

Evolutionary reversibility represents a strong test of the importance of contingency and determinism in evolution. If selection is limited in its ability to drive the reacquisition of ancestral forms, then the future outcomes available to evolution at any point in time must depend strongly on the present state and, in turn, on the past. Ready reversibility, in contrast, would indicate that natural selection can produce the same optimal form in any given environment, irrespective of history. The evolutionary reversibility of a protein can be evaluated at three levels: molecular sequence, protein function, and the structural/mechanistic underpinnings for that function. The latter is most relevant to understanding the roles of contingency and determinism in evolution. ... True reversal, involving restoration of the ancestral phenotype by the ancestral structure-function relations, would indicate that the forms of functional proteins can evolve deterministically, irrespective of contingent historical events.

After experimentally supporting the claim that a GR-like protein would be very unlikely to revert to an MR-like ancestral form by Darwinian means, they concluded:

We predict that future investigations, like ours, will support a molecular version of Dollo's law: as evolution proceeds, shifts in protein structure-function relations become increasingly difficult to reverse whenever those shifts have complex architectures, such as requiring conformational changes or epistatically interacting substitutions.

I think the experimental work of Bridgham et al (2009) is great, and I think their interpretive reasoning is fine as far as it goes. But it is severely pinched by their Darwinian framework; their results point to much more.
Just as for some general laws of physics, there is nothing inherently time-asymmetric about generic random mutation and selection. So there should be nothing particularly special about evolving back in history versus forward. The only thing that would be "special" about going back is that you can (potentially) know which way you had come, so you can see if the steps can be retraced, as Bridgham et al (2009) did. However, the huge roadblock that the authors discovered for one homologous protein converting to another by Darwinian processes did not have to be in the past -- the roadblock could as easily have been in the future. If the GR-like protein had come first in history, then no MR-like protein would likely have arisen by Darwinian means. In that case, however, there would have been no question even raised by investigators about the reversibility of that evolutionary path, because the "path" would not exist -- it would have been blocked at the start, in the forward direction. Questions do not arise about hypothetical pathways that would have to pass through brick walls.

The old, organismal, time-asymmetric Dollo's law supposedly blocked off just the past to Darwinian processes, for arbitrary reasons. A Dollo's law in the molecular sense of Bridgham et al (2009), however, is time-symmetric. A time-symmetric law will substantially block both the past and the future, for well-understood reasons: Natural selection fits a protein to a current, not any future (nor any previous), task; thus it tends strongly to restrict other potential structures/functions. The very same considerations ("shifts in protein structure-function relations", "epistatically interacting substitutions", and so on) that frustrate the reacquisition of complex molecular features will tend strongly to stymie their acquisition in the first place, because no potential protein component would ever be without a prior history of selection. A time-symmetric Dollo's law turns the notion of "pre-adaptation" on its head. The law instead predicts something like "pre-sequestration", where proteins that are currently being used for one complex purpose are very unlikely to be available for either reversion to past functions or future alternative uses.

Yet here we are, with complex life all around us and in us. If a time-symmetric Dollo's law were really such a big roadblock, how did life come to be? Here is where their Darwinian framework most seriously blinkers their vision. Bridgham et al (2009) aimed to test "the importance of contingency and determinism in evolution". But chance and necessity are not the only things that exist. There are also mind and plan. In fact, in their own work the authors themselves reconstructed the ancestral protein from the descendant protein, easily overcoming the hurdle that they realized would block a Darwinian process. Their own minds directed events that chance and necessity never could.